Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.

Experimental Study of Heat Transfer in an Insulated Local Heated fromBelow and Comparison with Simulation by Lattice Boltzmann Method

In this paper,experimental and numerical studies of heat transfer in a test local of side H=0.8 m heated from below are presented and compared.All the walls,the rest of the floor and the ceiling are made from plywood and polystyrene in sandwich form(3 mmplywood-3 cm polystyrene-3 mmplywood)just on one of the vertical walls contained a glazed door(2 H/3×0.15 m).This local is heated during two heating cycles by a square plate of iron the width L=0.6 H,which represents the heat source,its temperature Th is controlled.The plate is heated for two cycles by an adjustable set-point heat source placed just down the center of it.For each cycle,the heat source is switched“on”for 6 h and switched“off”for 6 h.The outdoor air temperature is kept constant at a low temperature Tc<Th.All measurements are carried out with k-type thermocouples and with flux meters.Results will be qualitatively presented for two cycles of heating in terms of temperatures and heat flux densitiesϕfor various positions of the test local.The temperature evolution of the center and the profile of the temperature along the vertical centerline are compared by two dimensions simulation using the lattice Boltzmann method.The comparison shows a good agreement with a difference that does not exceed±1℃.

From Knowledge Transfer to Capability Development:The Future of PBL+CBL Teaching Method in Operating Room Nursing Education

Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursing.Presently,the PBL(problem-based learning)pedagogical approach,when integrated with CBL(case-based learning),has garnered considerable interest.An extensive literature review has been conducted to analyze the application of the PBL-CBL fusion in the education of perioperative nursing.Findings indicate that this integrative teaching methodology not only enhances students’theoretical knowledge,practical competencies,and collaborative skills but also contributes to the elevation of teaching quality.In conclusion,the PBL-CBL teaching approach holds immense potential for broader application in perioperative nursing education.Nevertheless,it is imperative to continually refine this combined pedagogical strategy to further enhance the caliber of perioperative nursing instruction and to cultivate a greater number of exceptional nursing professionals in the operating room setting.

Amplitude and Period Effect on Heat Transfer in an Enclosure with Sinusoidal Heating from Below Using Lattice Boltzmann Method

This work presents a simulation of the phenomena of natural convection in an enclosure with a variable heating regime by the lattice Boltzmann method(LBM).We consider a square enclosure of side H filled with air(Pr=0.71)and heated from below,with a hot portion of length L=0.8 H,by imposing a sinusoidal temperature.The unheated segments of the bottom wall are treated as adiabatic,and one of the vertical walls features a cold region,while the remaining walls remain adiabatic.The outcomes of the two-dimensional(2D)problem are depicted through isotherms,streamlines,the temperature evolution within the enclosure,and the Nusselt number.These visualizations span various amplitude values“a”in the interval[0.2,0.8],and of the period T0 for Ra=107.The amplitude and period effect on the results is evaluated and discussed.The amplitude of the temperature at the heart of the enclosure increases with the increase in amplitude.This also increases with the period(T0)of the imposed temperature,something that is not observable on the global Nusselt number.

Impact of a Magnetic Dipole on Heat Transfer in Non-Conducting Magnetic Fluid Flow over a Stretching Cylinder

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered.The governing nonlinear differential equations are solved numerically using a finite element approach,which is properly validated through comparison with earlier results available in the literature.The results for the velocity and temperature fields are provided for different values of the Reynolds number,ferromagnetic response number,Prandtl number,and viscous dissipation parameter.The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated.The applicability of this research to heat control in electronic devices is discussed to a certain extent.

Numerical Predictions of Laminar Forced Convection Heat Transfer with and without Buoyancy Effects from an Isothermal Horizontal Flat Plate to Supercritical Nitrogen

Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing downwards.Computations are performed by varying the value ofΔT from5 to 30 K and P_(∞)/P_(cr)ratio from1.1 to 1.5.Variation of all the thermophysical properties of supercritical Nitrogen is considered.The wall temperatures are chosen in such a way that two values of Tw are less than T∗(T*is the temperature at which the fluid has a maximum value of Cp for the given pressure),one value equal to T∗and two values greater than T∗.Three different values of U∞are used to obtain Re∞range of 3.6×10_(4)to 4.74×10^(5)for forced convection without buoyancy effects and Gr_(∞)/Re^(2)_(∞)range of 0.011 to 3.107 for the case where buoyancy effects are predominant.Six different forms of correlations are proposed based on numerical predictions and are compared with actual numerical predictions.It has been found that in all six forms of correlations,the maximum deviations are found to occur in those cases where the pseudocritical temperature TT∗lies between the wall temperature and bulk fluid temperature.

LOW-THRUST ORBIT TRANSFER BY COMBINING GENETIC ALGORITHM WITH REFINED Q-LAW METHOD

A new orbit transfer method is presented by combining the genetic algorithm（GA）with the refined Q-law method.Considering the energy consumption,the relative thrust efficiency is introduced as a threshold deciding whether to thrust or coast.GA is used to achieve the global time-optimal orbit transfer.The trajectory optimization problem is transformed into the constraint parameter optimization problem,thus the nonlinear two-point boundary value problem is avoided.The refined Q-law method integrated with the fuzzy logic control is adopted for the end course,the vibration is avoided and the high precision is achieved.The numerical simulation of satellite orbit transfer is implemented.Results show that the new method can achieve the time-optimal orbit transfer and the low energy consumption,thus improving the transfer precision.

Transfer matrix method for determination of the natural vibration characteristics of elastically coupled launch vehicle boosters

The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.

Regularization Method to the Parameter Identification of Interfacial Heat Transfer Coefficient and Properties during Casting Solidification

The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.

Carbon matrix effects on the micro-structure and performance of Pt nanowire cathode prepared by decal transfer method

High performance cathode for polymer electrolyte membrane fuel cell was prepared by depositing Pt nanowires in a carbon matrix coated on a substrate, and using decal transfer method to fabricate the membrane electrode assembly. The effects of carbon and ionomer contents on the electrode micro-structure and fuel cell performance are investigated by physical characterization and single cell testing. The Pt nanowires are gradient distributed across the cathode thickness, and more Pt exists near the membrane. Both the carbon and ionomer contents can affect the Pt nanowires distribution and aggregation. In addition, the carbon loading dominates the transport distance of gas and proton, and the ionomer content affects the triple phase boundaries and porosity in the cathode. The optimal structure of Pt nanowire cathode is obtained at 0.10 mg·cm^-2 carbon loading and 10 wt% ionomer.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Analytical method of load-transfer of single pile under expansive soil swelling

The elastic differential equations of load-transfer of single pile either with applied loads on pile-top or only under the soil swelling were established,respectively,based on the theory of pile-soil interaction and the shear-deformation method.The derivation of analytic solution to load-transfer for single pile in expansive soil could hereby be obtained by means of superposition principle under expansive soils swelling.The comparison of two engineering examples was made to prove the credibility of the suggested method.The analyzed results show that this analytic solution can achieve high precision with few parameters required,indicating its' simplicity and practicability in engineering application.The employed method can contribute to determining the greatest tension along pile shaft resulting from expansive soils swelling and provide reliable bases for engineering design.The method can be employed to obtain various distributive curves of axial force,settlements and skin friction along the pile shaft with the changes of active depth,vertical movements of the surface and loads of pile-top.

Zonal method solution of radiative heat transfer in a one-dimensional long roller-hearth furnace in CSP

A radiative heat transfer mathematical model for a one-dimensional long furnace was set up in a through-type roller-hearth furnace （TTRHF） in compact strip production （CSP）. To accurately predict the heat exchange in the furnace, modeling of the complex gas energy-balance equation in volume zones was considered, and the heat transfer model of heating slabs and wall lines was coupled with the radiative heat transfer model to identify the surface zonal temperature. With numerical simulation, the temperature fields of gas, slabs, and wall lines in the furnace under one typical working condition were carefully accounted and analyzed. The fundamental theory for analyzing the thermal process in TI＇RI-IF was provided.

A Numerical Method on Inverse Determination of Heat Transfer Coefficient Based on Thermographic Temperature Measurement

The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.

Study of heat transfer by using DEM–CFD method in a randomly packed pebble-bed reactor

The pebble-bed reactor is one of the most promising designs for the nuclear energy industry. In this paper,a discrete element method-computational fluid dynamics(DEM-CFD) approach that includes thermal conduction, radiation, and natural convection mechanisms was proposed to simulate the thermal-fluid phenomena after the failure of forced circulation cooling system in a pebble-bed core. The whole large-scale packed bed was created using the DEM technique, and the calculated radial porosity of the bed was validated with empirical correlations reported by researchers. To reduce computational costs, a segment of the bed was extracted, which served as a good representative of the large-scale packed bed for CFD calculation. The temperature distributions simulated with two different fluids in this DEM-CFD approach were in good agreement with SANA experimental data. The influence of the natural convection mechanism on heat transfer must be taken into account for coolants with strong convective capacity. The proposed DEM-CFD methodology offers a computationally efficient and widely applied method for understanding the heat transfer process in a pebble-bed core. The method can also be easily extended to assess the passive safety features of newly designed fluoride-salt-cooled pebble-bed reactors.

Dynamics Analysis of a Parallel Mill-turn Tool Spindle Head Driven by Dual-linear Motors Using Extended Transfer Matrix Method

The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine tool application,due to the difficulty of solving the hybrid equations or the limitation of current software when dealing with the hybrid dynamics.The extended transfer matrix method（E-TMM）,which extends elements in three-dimensional space with higher matrixes,is proposed to simplify the modeling process of the hybrid dynamics.The E-TMM modeling approaches of 3 basic elements including 3D vibrant rigid body,joint and flexible body are studied in details.A parallel mill-turn tool spindle head unit driven by dual-linear motors is chosen as a plant to demonstrate the E-TMM modeling process.By using E-TMM,the spindle head unit is simplified as a topological network consisting of the three types of element,i.e.,3D vibrant rigid body,joint and flexible body,including 11 rigid bodies,14 joints and 1 3D-Timoshenko beam.Then the dynamic model of the system can be easily obtained by deducing the element-network by means of state vector transformation.The dynamic characteristics of the spindle head,such as natural frequencies,dynamic flexibility,etc.can be predicted by solving the obtained model.Experiment verification indicates that the E-TMM is valid with enough accuracy in the dynamic analysis of the parallel mill-turn tool spindle head.The E-TMM is capable of modeling the dynamics of machine tool structure with no requirements of deducing and solving the sophisticated differential equations.Moreover,the E-TMM provides a simple and elegant tool for hybrid dynamic analysis in future dynamic design of machine tools.

Numerical Simulation of Fluid and Heat Transfer in a Biological Tissue Using an Immersed Boundary Method Mimicking the Exact Structure of the Microvascular Network

The aim of this study is to develop a model of fluid and heat transfer in a biological tissue taking into account the exact structure of the related microvascular network,and to analyze the influence of structural changes of such a network induced by diabetes.A cubic region representing local skin tissue is selected as the computational domain,which in turn includes two intravascular and extravascular sub-domains.To save computational resources,the capillary network is reduced to a 1D pipeline model and embedded into the extravascular region.On the basis of the immersed boundary method(IBM)strategy,fluid and heat fluxes across a capillary wall are distributed to the surrounding tissue nodes by a delta function.We consider both steady and periodic blood pressure conditions at the entrances of the capillary network.Under steady blood pressure conditions,both the interstitial fluid pressure and tissue temperature around the capillary network are larger than those in other places.When the periodic blood pressure condition is considered,tissue temperature tends to fluctuate with the same frequency of the forcing,but the related waveform displays a smaller amplitude and a certain time(phase)delay.When the connectivity of capillary network is diminished,the capacity of blood redistribution through the capillary network becomes weaker and a subset of the vessel branches lose blood flow,which further aggravates the amplitude attenuation and time delay of the skin temperature fluctuation.

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

Vibration analysis of fluid- structure interaction in water hammer based on transfer matrix method

In consideration of the problem that the effect of conduit structure on water hammer has been ignored in the classical theory,the Poisson coupling between the fluid and the pipeline was studied and a fourteen-equation mathematical model of fluid-structure interaction(FSI)was developed.Then,the transfer matrix method(TMM)was used to calculate the modal frequency,modal shape and frequency response.The results were compared with that in experiment to verify the correctness of the TMM and the results show that the fluid-structure coupling has a greater impact on the modal frequencies than the modal shape.Finally,the influence on the response spectrum of different damping ratios was studied and the results show that the natural frequency under different damping ratios has changed little but there is a big difference for the pressure spectrum.With the decreasing of damping ratio,the damping of the system on frequency spectrum is more and more significant and the dispersion and dissipation is more and more apparent.Therefore the appropriate damping ratio should be selected to minimize the effects of the vibration of the FSI.The results provide references for the theory research of FSI in the transient process.